319handout6 - X and Y is given by f x;y =& 2 5(2 x 3 y...

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Econ 319, Fall 2008 TA: Simon Kwok Handout 6 1. Recall that the probability function obtained in handout 4, question 4 is f ( x ) = 8 > > > > < > > > > : 0 : 4 if x = ° 2 0 : 1 if x = 0 0 : 3 if x = 1 0 : 2 if x = 4 0 otherwise : Find (a) E ( X ) ; (b) V ar ( X ) : 2. Recall that the probability density function (pdf) obtained in handout 4, question 3(b) is f ( x ) = ° 8 9 (2 x ° x 2 ) if 0 < x < 3 2 0 otherwise. : Find (a) E ( X ) ; (b) V ar ( X ) : 3. For the continuous uniform distribution of X with pdf f ( x ) = ° 1 ° ° ± if ° < x < ± 0 otherwise. , prove that (a) E ( X ) = ± + ° 2 : (b) V ar ( X ) = ( ° ° ± ) 2 12 : 4. Recall from handout 5, question 1 that the pdf of the joint distribution of
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Unformatted text preview: X and Y is given by f ( x;y ) = & 2 5 (2 x + 3 y ) ; ± x;y ± 1 ; otherwise : Find (a) E ( X ) and E ( Y ) ; (b) V ar ( X ) and V ar ( Y ) ; (c) Cov ( X; Y ) . 5. Let X be a random variable that is uniformly distributed on the interval [-1,1]. Find (a) E ( X ) ; (b) E ( X 2 ) ; (c) V ar ( X 2 ) ; (d) E ( j X j ) : 1...
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